Chapter 5-1

Perpindiculars and Bisectors and Altitudes

Perpendicular Bisector Theorem: a point that lies on the perpendicular bisector of a segment is equidistant from endpoints of the segment.

Converse of the Perpendicular Bisector Theorem: if a point is equidistant from the endpoints of the segment, then it is on the perpendicular bisector of the segment.

Concurrent Lines: three or more lines (or rays or segments) that intersect at the same point.

Perpendicular Bisector of a Triangle: a line (or ray or segment) that is perpendicular to the side of a triangle at the midpoint of a side.

Circumcenter Theorem: the circumcenter is equidistant from the vertices.

Angle Bisector of a triangle: bisector of an angle of the triangle

point of concuraccy: incenter

Incenter theorem: the incenter is equidistant from the sides

Median of a Triangle: segment whose endpoints are a vertex and the midpoint of the opposite side

Point of concurracy: centroid

Centroid Theorem: from the centroid to the side is half the distance to the angle.

Altitude of a triangle: the perpendicular segment from a vertex to the opposite side, or the extension of that side

Point of concurracty: orthocenter